黑龙江省哈尔滨市第三中学校2022-2023学年高二上学期第二次验收考试英语试卷Word版含答案
2022年黑龙江省哈尔滨市新第三中学高二英语模拟试卷含解析
2022年黑龙江省哈尔滨市新第三中学高二英语模拟试卷含解析一、选择题1. I shall never forget those years ________I lived in the country with farmers，________has a great effect on my life.A．that；which B．when；which C．which；that D．when；who参考答案：B2. —Mum, I can’t see any point in studying hard.—Come on, dear. Years of hard study will surely ______ in your future career.A. make sureB. pay offC. bring backD. pay back参考答案：B略3. Information has been put forward______ more middle school graduates will be admitted into universities.A. whileB. thatC. whichD. this参考答案：B4. ______ huge number of people are speaking Chinese as _____ foreign language.A. The; /B. A; /C. A; aD. The; a参考答案：C略5. In the eyes of a policeman, it’s usually dangerous to get close to the_______ criminal. He may do anything he would to escape.A. sensitiveB. consciousC. primitiveD. desperate参考答案：D【详解】考查形容词辨析。
黑龙江省哈尔滨市第三中学校2022-2023学年高二下学期期末考试英语试题
黑龙江省哈尔滨市第三中学校2022-2023学年高二下学期期末考试英语试题学校:___________姓名：___________班级：___________考号：___________一、短对话1．Where is the hairdryer?A．In the bedroom.B．In the bathroom.C．In the sitting room. 2．What is the man doing?A．Expressing thanks.B．Asking for help.C．Making a suggestion. 3．What are the speakers talking about?A．A bus line.B．A policy.C．A newspaper. 4．What does the man suggest the woman do?A．Shop online.B．Take a day off.C．Borrow a coffeemachine.5．What is the probable relationship between the speakers?A．Relatives.B．Classmates.C．Colleagues.二、长对话听下面一段较长对话，回答以下小题。
6．How does the man usually go to work?A．By car.B．By bike.C．By subway.7．What will the man start doing next month?A．Learning to drive.B．Travelling around the world.C．Looking for a new apartment.听下面一段较长对话，回答以下小题。
8．At what price was The Scream sold?A．82.5 million dollars.B．106.5 million dollars.C．119.9 million dollars. 9．What does the woman say about the paintings?A．Their commercial value always changes.B．They’re becoming more valuable than before.C．They get much appreciation from personal collectors.听下面一段较长对话，回答以下小题。
黑龙江省哈尔滨市第三中学校2024-2025学年高二上学期期中考试数学及答案
哈三中2024—2025学年度上学期高二学年期中考试数学试卷考试说明：（1）本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，满分150分.考试时间为120分钟；（2）第Ⅰ卷，第Ⅱ卷试题答案均答在答题卡上，交卷时只交答题卡.第Ⅰ卷（选择题，共58分）一、选择题（共58分）（一）单项选择题（共8小题，每小题5分.在每小题给出的四个选项中，只有一项是符合题目要求的）1．圆()()22342x y +++=的圆心和半径分别是（）A ．()3,4-，2B ．()3,4-，2C ．()3,4--D ．()3,4-2．下列命题是真命题的是（）A ．经验回归方程 y bxa =+ 至少经过其样本数据点()11,x y ，()22,x y ，…，(),n n x y 中的一个B ．可以用相关系数r 来刻画两个变量x 和y 线性相关程度的强弱，r 的绝对值越小，说明两个变量线性相关程度越强C ．线性回归分析中决定系数用2R 来刻画回归的效果，若2R 值越小，则模型的拟合效果越好D ．残差点分布在以横轴为对称轴的水平带状区域内，该区域越窄，拟合效果越好3．某市高中数学统考中，甲、乙、丙三所学校的数学成绩分别服从正态分布()11,N μσ，()22,N μσ，()33,N μσ，其正态分布的密度曲线如图所示，则（）A ．123μμμ=>B ．123μμμ=<C ．123μμμ>=D ．123μμμ<=4．将1，2，3，4，5，6这6个数填入如图所示的3行2列表格中，则表格内每一行数字之和均相等的概率为（）A ．16B ．112C ．115D ．1305．设a 为实数，已知直线1l ：310ax y a +++=，2l ：()6340x a y +-+=，若12l l ∥，则a =（）A ．6B ．3-C ．6或3-D ．6-或36．已知直线l ：410x ty +-=，其中t 为321x x ⎛⎫+ ⎪⎝⎭展开式中的常数项，则点()2,1P 到直线l的距离为（）A ．1B ．2C ．5D ．107．某学校为了解校庆期间不同时段的校门人流量，从上午8点开始第一次反馈校门人流量，以后每过2小时反馈一次，共统计了前3次的数据(),i i y ，其中1i =，2，3，i y 为第i 次人流量数据（单位：千人），由此得到y 关于i 的回归方程 26log y i a=+.已知4y =，根据回归方程，可预测下午2点时校门人流量为（）千人.参考数据：2log 3 1.6≈A ．9.6B ．10.8C ．12D ．13.28．已知函数()11,0231,01x x f x x x x ⎧-+<≤⎪⎪=⎨+⎪≤⎪-+⎩，则()9723f x x --的取值范围为（）A ．404,,2121⎛⎤⎡⎫-∞-+∞ ⎪⎥⎢⎝⎦⎣⎭ B ．220,,33⎛⎤⎡⎫-∞-+∞ ⎪⎥⎢⎝⎦⎣⎭ C ．[)40,0,21⎛⎤-∞-+∞ ⎥⎝⎦ D ．()20,0,3⎡⎫-∞+∞⎪⎢⎣⎭（二）多项选择题（共3小题，每小题6分.在每小题给出的选项中，有多项符合题目要求，全部选对的得6分，部分选对的得部分分，有选错的得0分）9．关于函数()ππsin 2cos 266f x x x ⎛⎫⎛⎫=+++ ⎪ ⎪⎝⎭⎝⎭，下列命题中正确的是（）A ．()y f x =是以π为最小正周期的周期函数B ．()y f x =C ．将函数2y x =的图象向左平移7π24个单位后，与已知函数的图象重合D ．()y f x =的图象关于直线π24x =对称10．在平面直角坐标系中，定义(){}1212,max ,d A B x x y y =--为两点1,1，2,2的“切比雪夫距离”，又设点P 及直线l 上任意一点Q ，称(),d P Q 的最小值为点P 到直线l 的“切比雪夫距离”，记作(),d P l ，则下列命题中正确的是（）A ．12,6M ⎛⎫- ⎪⎝⎭，4,13N ⎛⎫-- ⎪⎝⎭，则()7,6d M N =B ．O 为坐标原点，动点R 满足(),1d O R =，则R 的轨迹为圆C ．对任意三点A 、B 、C ，都有()()(),,,d C A d C B d A B +≥D ．已知点()1,3P 和直线l ：210x y -+=，则()4,3d P l =11．高考数学试题第二部分为多选题，共3个小题，每小题有4个选项，其中有2个或3个是正确选项，全部选对得6分，部分选对得部分分，有选错的得0分.若正确答案是2个选项，只选对1个得3分，有选错的得0分；若正确答案是3个选项，只选对1个得2分，只选对2个得4分，有选错的得0分.小明对其中的一道题完全不会，该题有两个正确选项的概率是23，记X 为小明随机选择1个选项的得分，记Y 为小明随机选择2个选项的得分，则（）A ．()()()346P X P Y P Y ===+=B ．()()E Y E X <C ．()74D X =D ．()()294E X D X -=第Ⅱ卷（非选择题，共92分）二、填空题（本大题共3小题，每小题5分，共15分.将答案填在答题卡相应的位置上）12．下列说法中正确的有（填正确说法的序号）10y ++=的倾斜角为2π3②直线1x +=③直线()23y a x a =-+（a ∈R ）过定点()3,6-④点()0,1到直线20y +=的距离为113．对于随机事件,M N ，若()12P M =，()34P M N =，()38P M N =，则()P N =.14．已知正方体1111ABCD A B C D -的棱长为2，E 、F 为空间内两点且12AE AD =，BF BA BC λμ=+，[],0,1λμ∈.当三棱锥11A FC E -的体积最大时，其外接球的表面积为.三、解答题（本大题共5小题，共77分.解答应写出文字说明、证明过程或演算步骤）15．ABC V 的内角A ，B ，C 的对边分别为a ，b ，c )cos cos 2sin b C c B a A +=(1)求锐角A 的大小；(2)在（1）的条件下，若sin cos C C =，且ABC V 的周长为求ABC V 的面积.16．已知ABC V 的三个顶点分别是()2,1A ，()1,0B -，()3,3C (1)求边AC 的高BH 所在直线方程；(2)已知M 为AB 中点，试在直线CM 上求一点P ，在x 轴上求一点Q ，使APQ △的周长最小，并求最小值.17．随着冬天的临近，哈尔滨这座冰雪之城，将再次成为旅游的热门目的地.为更好地提升旅游品质，我市文旅局随机选择100名青年游客对哈尔滨出行体验进行满意度评分（满分100分），80分及以上为良好等级，根据评分，制成如图所示的频率分布直方图.(1)根据频率分布直方图，求x 的值并估计该评分的上四分位数；(2)若采用按比例分层抽样的方法从评分在[)70,80，[)80,90的两组中共抽取6人，再从这6人中随机抽取4人进行单独交流，求选取的4人中评分等级为良好的人数X 的分布列和数学期望；(3)为进一步了解不同年龄段游客对哈尔滨出行体验的反馈，我市文旅局再次随机选择100名中老年游客进行满意度评分，发现两次调查中评分为良好等级的人数为120名.请根据小概率值0.001α=的独立性检验，分析游客的评分等级是否良好与年龄段（青年或中老年）是否有关.附：()()()()()22n ad bc a b c d a c b d χ-=++++，n a b c d=+++α0.050.010.001x α3.8416.63510.82818．棱长为2的正方体1111ABCD A B C D -，M 为正方体中心，将四棱锥11M BCC B -绕1CC 逆时针旋转α（0πα<<）后得到四棱锥11M B CC B '''-，如图1.(1)求四棱锥11M BCC B -的表面积和体积；(2)若π2α=（如图2），求证：平面1MBB⊥平面1M B B'''；(3)求α为多少时，直线1M B''与直线DC所成角最小，并求出最小角的余弦值.19．某志愿者社团计划在周一和周二两天各举行一次活动，分别由甲、乙两人负责活动通知，已知该社团共有n位同学，每次活动均需k位同学参加.假设甲和乙分别将各自活动通知的信息独立、随机地发给该社团k位同学，且所发信息都能收到.(1)当8n=，3k=时，求该社团只有小明同学同时收到甲、乙两人所发活动通知信息的概率；(2)记至少收到一个活动通知信息的同学人数为X①设5n=，2k=，求随机变量X的分布列和数学期望；②求使()P X m=取得最大值的整数m.1．C【分析】由圆的标准方程直接可得出圆的圆心和半径.【详解】圆()()22342x y +++=的圆心为()3,4--.故选：C.2．D【分析】根据经验回归方程、相关系数、决定系数、残差等知识确定正确答案.【详解】对于A ，经验回归方程ˆˆˆybx a =+是由最小二乘法计算出来的，它不一定经过其样本数据点，一定经过)(x y ，所以A 错误；对于B ，由相关系数的意义，当r 越接近1时，表示变量y 与x 之间的线性相关程度越强，所以B 错误；对于C ，用决定系数2R 的值判断模型的拟合效果，2R 越大，模型的拟合效果越好，所以C 是错误；对于D ，因为在残差的散点图中，残差分布的水平带状区域的宽度越窄，表明数据越集中，模型的拟合效果越好，故D 正确.故选：D.3．D【分析】根据给定的曲线，利用正态分布的密度曲线的特征判断即得.【详解】观察曲线知，123μμμ<=.故选：D 4．C【分析】根据题意，先将6个数字分为3组，再将三组全排列，安排在表格的三行中，由分步计数原理计算计算个数，即可由古典概型概率公式求解.【详解】要使表格内每一行数字之和均相等，根据162534+=+=+，先将6个数字分为3组，分别为(1,6)，(2,5)，(3,4)；将三组全排列，安排在表格的三行中，每一行有22A 种顺序，则可组成不同表格的个数为22232223A A A A 48=；将1，2，3，4，5，6这6个数填入表格中的所有情况66A 720=,故概率为48172015=故选：C ．5．A【分析】由题可得()318a a -=，据此可得a 的可能值，验证后可得答案.【详解】因12l l ∥，则()()()23183180630a a a a a a -=⇒--=⇒-+=.则6a =或3a =-.当6a =，1l ：6370x y ++=，2l ：6340++=x y ，满足12l l ∥；当3a =-，1l ：3320x y -+-=，2l ：66403320x y x y -+=⇔-+-=，两直线重合，不合题意.则6a =.故选：A 6．B【分析】根据二项式展开式的通项特征可得3t =，即可根据点到直线的距离公式求解.【详解】321x x ⎛⎫+ ⎪⎝⎭展开式的常数项为12321C 3x x ⎛⎫= ⎪⎝⎭,故3t =，所以直线l ：4310x y +-=，故点()2,1P 到直线l 2=，故选：B 7．B【分析】令2log x i =，由 6y x a =+，求出 a ，得回归方程，可求预测值.【详解】令2log x i =，则6y x a =+ ，222log 1log 2log 3 2.633x ++==，又4y =，由 6y x a =+，得 2.6463a =⨯+，所以 1.2a =-，则 26log 1.2y i =-，下午2点时对应4i =，可得 26log 4 1.210.8y =-=.故选：B.8．B【分析】化简()f x ，()9723f x x --函数()f x 上一点()(),x f x 与39,27A ⎛⎫⎪⎝⎭连线斜率k 的72-倍，求出k 的范围，即可得出答案.【详解】因为()11,02321,01x x f x x x ⎧-+<≤⎪⎪=⎨⎪-≤⎪-⎩，图象如下图，()12,,0,13B C ⎛⎫⎪⎝⎭，()()()9979777733232222f x f x f x x x x ⎡⎤---⎢⎥-⎣⎦==-⋅-⎛⎫-- ⎪⎝⎭，表示函数()f x 上一点()(),x f x 与39,27A ⎛⎫⎪⎝⎭连线斜率k 的72-倍，()12,,0,13B C ⎛⎫⎪⎝⎭，91204073213121222AB k -===---，9214773321022AC k -===-，由图可知：421k ≥或4021k ≤-，所以7223k -≤-或72023k -≥，则()9723f x x --的取值范围为220,,33∞∞⎛⎤⎡⎫--⋃+ ⎪⎥⎢⎝⎦⎣⎭.故选：B.9．ABD【分析】根据辅助角公式可得()5π212f x x ⎛⎫=+ ⎪⎝⎭，即可根据周期以及最值求解AB ，根据平移的性质即可判断C ，代入验证即可求解D.【详解】()ππππ5πsin 2cos 222666412f x x x x x ⎛⎫⎛⎫⎛⎫⎛⎫=+++=++=+ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭,对于A ，最小正周期为2ππ2=，A 正确，对于B ，由于5πsin 212x ⎛⎫+ ⎪⎝⎭的最大值为1，故()y f x =B 正确，对于C，2y x =的图象向左平移7π24个单位后，得到()7π7π224212x f x y x ⎛⎫⎛⎫=+≠ ⎪ ⎪⎝⎝⎭=+⎭，故C 错误，对于D ，5ππ22ππ214242f ⎛⎫⎛⎫=⨯+== ⎪ ⎪⎝⎭⎝⎭，故()y f x =的图象关于直线π24x =对称，D 正确，故选：ABD 10．ACD【分析】对于A ：根据切比雪夫距离的定义直接运算即可；对于B ：设(),R x y ，分析可得11x y ⎧≤⎪⎨≤⎪⎩，且等号至少有一个成立，即可得结果；对于C ：根据题意结合绝对值不等式的分析判断；对于D ：设点(,21)Q x x -可得{}(,)max 3,22d P Q x x =--，讨论可得距离d ，再由函数的性质，求得最小值.【详解】对于选项A ：若12,6M ⎛⎫- ⎪⎝⎭，4,13N ⎛⎫-- ⎪⎝⎭，则()4217213366⎛⎫---=--= ⎪⎝⎭，因为2736<，所以()7,6d M N =，故A 正确；对于选项B ：设(),R x y ，若(),1d O R =，则11x y ⎧≤⎪⎨≤⎪⎩，且等号至少有一个成立，可得R 的轨迹如图所示，为正方形，故B 错误；对于选项C ：设112233(,),(,),(,)A x y B x y C x y ，则{}{}13133232(,)(,)max ,max ,d A C d C B x x y y x x y y +=--+--133212x x x x x x ≥-+-≥-，同理可得12(,)(,)d A C d C B y y +≥-，所以{}1212(,)(,)max ,(,)d A C d C B x x y y d A B +≥--=，故C 正确；对于选项D ：设(,21)Q x x -为直线:210l x y --=上一点，则{}(,)max 3,22d P Q x x =--，当322x x -≥-，即513x -≤≤时，则(,)3d P Q x =-，可知当53x =时，取得最小值43；当322x x -<-，即53x >或1x <-，则4(,)223d P Q x =->，无最小值；综上可得：4(,)3d P l =，故D 正确；故选：ACD.【点睛】方法点睛：“新定义”主要是指即时定义新概念、新公式、新定理、新法则、新运算五种，然后根据此新定义去解决问题，有时还需要用类比的方法去理解新的定义，这样有助于对新定义的透彻理解.对于此题中的新概念，对阅读理解能力有一定的要求.但是，透过现象看本质，它们考查的还是基础数学知识，所以说“新题”不一定是“难题”，掌握好三基，以不变应万变才是制胜法宝.11．BCD【分析】分别计算出X 和Y 的分布列，然后逐项进行计算即可求得.【详解】由题意，X 0=，若该题有两个正确选项，则小明从两个错误选项中选择1个；若该题有3个正确选项，则小明从1个错误选项中选择1个，概率为：()11211144C C 21503C 3C 12P X ==⨯+⨯=；2X =，该题有3个正确选项，则小明从3个正确选项中选择1个，概率为：()1314C 1123C 4P X ==⨯=；3X =，该题有2个正确选项，则小明从2个正确选项中选择1个，概率为：()1214C 2133C 3P X ==⨯=；Y 0=，若该题有两个正确选项，则小明从两个错误选项中选择1个或选择2个错误选项；若该题有3个正确选项，则小明从1个错误选项中选择1个，再从3个正确选项中选一个，概率为：()1111231222222444C C C C C 2211303C 3C 3C 18P Y ==⨯+⨯⨯=；4Y =，该题有3个正确选项，则小明从3个正确选项中选择2个，概率为：()2324C 1143C 6P Y ==⨯=；6Y =，该题有2个正确选项，则小明从2个正确选项中选择2个，概率为：()2224C 2163C 9P Y ==⨯=；对于A 选项，()()()15346318P X P Y P Y ==≠=+==，A 错误；对于B 选项，()511302312432E X =⨯+⨯+⨯=；()1311404618693E Y =⨯+⨯+⨯=；所以()()E Y E X <，B 正确；对于C 选项，()251104941243E X=⨯+⨯+⨯=，()()()()22237424D X E X E X ⎛⎫=-=-= ⎪⎝⎭，C 正确；对于D 选项，()()279444E XD X -=-=，D 正确.故选：BCD.12．①③【分析】对于①，根据斜率与倾斜角的关系可判断，对于②，将直线化为一般式，即可判断；对于③，将直线()23y a x a =-+化为()()236y a x =-++，故可判断；对于④，根据点到直线的距离公式即可判断.10y ++=的斜率为根据倾斜角θ满足tan πθθ=≤<，即2π3θ=，故①正确；对于②，将直线1x +=0y +=，所以斜率为对于③，将直线()23y a x a =-+化为()()236y a x =-++，所以3x =-时，6y =，不论a 取值，故直线过定点()3,6-，故③正确；3=，故④错误.故答案为：①③13．13【分析】根据条件概率公式及概率的性质计算即可.【详解】因为()()()34P MN P M N P N ==，所以()()34P MN P N =，则()()()()()34P N P MN P MN P MN P N =+=+，所以()()14P MN P N =，又()()()()()()()1318P MN P M P N P MN P M N P N P N --+===-，所以()()()11132418P N P N P N --+=-，解得()13P N =.故答案为：13.14．11π【分析】根据条件得到E 为AD 中点，F 在平面ABCD 内，其中11A C E S V 为定值，只需点F 到平面11A C E 的距离最大，建立空间直角坐标系，设(),,0F s t ，[],0,2s t ∈，得到平面11A C E 的法向量，利用点到平面距离的向量公式得到当2s t ==时，点F 到平面11A C E 的距离最大，此时F 与B 重合，求出1DB ⊥平面11A BC ，设球心(),,O a b c ，由11OE OB OA OC ===得到方程组，求出球心和半径，求出表面积.【详解】因为12AE AD = ，所以E 为AD 中点，又BF BA BC λμ=+ ，[],0,1λμ∈，故F 在平面ABCD 内，其中11A C E S V 为定值，只需点F 到平面11A C E 的距离最大，以D 为坐标原点，1,,DA DC DD 所在直线分别为,,x y z 轴，建立空间直角坐标系，正方体1111ABCD A B C D -的棱长为2，故()()()()112,0,2,1,0,0,0,2,2,2,2,0A E C B ，设(),,0F s t ，[],0,2s t ∈，设平面11A C E 的法向量为(),,m x y z = ，则()()()()111,,1,0,220,,2,2,0220m A E x y z x z m A C x y z x y ⎧⋅=⋅--=--=⎪⎨⋅=⋅-=-+=⎪⎩，令1z =得2,2x y =-=-，故()2,2,1m =-- ，则(),,0F s t 到平面11A C E 的距离12223EF m d s t m ⋅==-- ，故当2s t ==时，点F 到平面11A C E 的距离最大，此时()2,2,0F ，即F 与B 重合，设球心(),,O a b c ，由11OE OB OA OC ===得()()()()()()()()()222222222222222222122122122a b c a b c a b c a b c a b c a b c ⎧-++=-+-+⎪⎪-++=-++-⎨⎪-++=+-+-⎪⎩，解得76a b c ===，故外接球球心为777,666O ⎛⎫⎪⎝⎭，，半径为r ==故外接球表面积为24π11πr =.故答案为：11π【点睛】方法点睛：几何体外接球问题，通常要找到几何体的一个特殊平面，利用正弦定理，几何性质找到其外心，求出外接圆的半径，进而找到球心的位置，进而求出半径，也可以利用空间向量的方放，设出球心坐标，待定系数法进行求解15．(1)π3A =(2)3【分析】（1）利用正弦定理化边为角，再结合两角和的正弦公式即可得解；（2）先求出C ，再根据正弦定理，令sin sin sin a b c k A B C===，求出,,a b c ，再根据三角形的周长求出k ，再根据三角形的面积公式即可得解.【详解】（1)cos cos 2sin b C c B a A +=，)sin cos sin cos 2sin sin B C C B A A +=，()2sin sin B C A A A +==，又sin 0A >，所以sin 2A =，又π0,2A ⎛⎫∈ ⎪⎝⎭，所以π3A =；（2）因为sin cos C C =，所以tan 1C =，又()0,πC ∈，所以π4C =，则()1sin sin 2B A C =+==，由正弦定理，令sin sin sin a b c k A B C===，则sin ,sin ,sin 242a k A kb k B kc k C k ======，所以ABC V 的周长为242a b c k ⎫++=++=+⎪⎪⎝⎭，解得4k =，所以a b ==所以1sin 32ABC S ab C ==V 16．(1)210x y ++=(2)当5,03Q ⎛⎫ ⎪⎝⎭时，APQ △.【分析】（1）求出边AC 的高BH 的斜率，再由点斜式方程即可得出答案.（2）先求出直线CM 的方程，如图，作出()2,1A 关于直线CM 的对称点(1,2)N ，作出()2,1A 关于x 轴的对称点(2,1)E -，则连结EN ，交直线CM 于P ，交x 轴于Q ，则MPQ V 的周长的最小值等于NE ，最后求出直线NE 的方程，即可求出点Q .【详解】（1）因为()2,1A ，()3,3C ，所以31232AC k -==-，所以边AC 的高BH 的斜率为12k =-，又因为直线BH 过点()1,0B -，所以BH 所在直线方程为：()112y x =-+，化简可得：210x y ++=.所以BH 所在直线方程为210x y ++=.（2）因为M 为AB 中点，所以11,22M ⎛⎫ ⎪⎝⎭，()3,3C ，直线CM 的方程为：33113322y x --=--，化简可得：y x =，如图，作出()2,1A 关于直线:0CM l x y -=的对称点(),N a b ，则1122122b a a b -⎧=-⎪⎪-⎨++⎪=⎪⎩，解得：1,2a b ==，所以()1,2N ，作出()2,1A 关于x 轴的对称点(2,1)E -，连结EN ，交直线CM 于P ，交x 轴于Q ，AP PN = ，AQ QE =，三角形APQ △的周长为线段NE 的长，由两点间线段最短得此时APQ △的周长最小，APQ △的周长最小时，最小值为：||NE =此时直线NE 的斜率为()21312--=--，直线NE 的方程为：()231y x -=--，化简可得：350x y +-=，令0y =，所以53x =，所以5,03Q ⎛⎫ ⎪⎝⎭，所以当5,03Q ⎛⎫ ⎪⎝⎭时，APQ △.17．(1)0.03x =，93.75(2)分布列见解析，()83E X =(3)无法认为游客的评分等级是否良好与年龄段有关.【分析】（1）根据频率和为1计算出x 的值；先判断出上四分位数所在区间，然后结合区间端点值以及该组的频率完成计算；（2）先根据分层抽样计算出每组抽取的人数，然后确定出X 的可取值并计算对应概率，由此可求分布列和数学期望；（3）根据已知条件得到对应22⨯列联表，然后计算出2χ的值并与对应x α比较大小，由此得到结论.【详解】（1）由频率分布直方图可知，0.005100.010100.01510100.040101x ⨯+⨯+⨯++⨯=，解得0.03x =；因为[]90,100的频率为100.0400.40.25⨯=>，且[]90,100为最后一组，所以评分的上四分位数位于区间[]90,100中，所以上四分位数为：0.40.25901093.750.4-+⨯=；（2）评分在[)70,80与[)80,90两组的频率分别为0.15,0.3，所以[)70,80内抽取人数为0.15620.150.3⨯=+，[)80,90内抽取人数为0.3640.150.3⨯=+，故6人中评分等级为良好的有4人，由题意可知，X 的可取值为2,3,4，()222446C C 22C 5P X ===，()132446C C 83C 15P X ===，()4446C 14C 15P X ===，所以X 的分布列为：X234P 25815115数学期望()2818234515153E X =⨯+⨯+⨯=；（3）青年游客评分等级良好的有()0.30.410070+⨯=人，所以老年游客评分等级良好的有1207050-=人，由上可得如下22⨯列联表，青年游客老年游客总计评分等级良好7050120评分等级非良好305080总计100100200零假设0H ：游客的评分等级是否良好与年龄段无关，由表中数据可得()220.001200350015008.33310.82810010080120x χ-=≈<=⨯⨯⨯，根据小概率值0.001α=的独立性检验，可知零假设0H 成立，即无法认为游客的评分等级是否良好与年龄段有关.18．(1)表面积为4，体积为43(2)证明见解析(3)π4α=时，直线1M B ''与直线DC 所成角最小，最小角的余弦值为3【分析】（1）根据棱锥的表面积公式和体积公式计算即可；（2）易得平面11DCC D ､平面11CB B C ''为同一个平面，补全正方体111BNB C B PB C ''-，证明111D B B ∠'为二面角111D BB B '--的平面角，再证明111π2D B B '∠=即可；（3）以C 为原点，建立空间直角坐标系，利用向量法求解即可.【详解】（1）由题意，MB =则1122MBB S =⨯=V所以四棱锥11M BCC B -的表面积为224⨯=，四棱锥11M BCC B -的高为1，则111422133M BCC B V -=⨯⨯⨯=；（2）若π2α=，则平面11DCC D ､平面11CB B C ''为同一个平面，如图，补全正方体111BNB C B PB C ''-，连接BD 、1BB '，则M 是BD 中点，M '是1BB '中点，所以平面1MBB 与平面11BDD B 重合，平面1M B B '''与平面11BB B B ''重合，由正方体性质可知1BB ⊥平面1111A B B D '，因为1111,B D B B '⊂平面1111A B B D '，所以111BB B D ⊥，111BB B B '⊥，111D B B ∠'为二面角111D BB B '--的平面角，因为1111111,2πD C B C D C B =∠=，则111π4D B C ∠=，同理可得111π4B B C '∠=，所以111π2D B B '∠=，所以平面1MBB ⊥平面1M B B '''；（3）如图，以C为原点，建立空间直角坐标系，则()()()10,0,0,0,2,0,2cos ,2sin ,2C D B αα'-，ππ,144M αα⎫⎛⎫⎛⎫-- ⎪ ⎪⎪⎝⎭⎝⎭⎭'，即()cos sin ,sin cos ,1M αααα+-'，故()()10,2,0,cos sin ,sin cos ,1DC M B αααα''==-+ ，则111cos ,DC M B DC M B DC M B '''⋅=='='' ，因为0πα<<，所以ππ5π444α<+<，所以πsin 4α⎛⎤⎛⎫+∈ ⎥ ⎪ ⎝⎭⎝⎦，所以1cos ,DC M B '=⎝⎦' ，所以1max cos ,DC M B ''= ，此时ππ42α+=，即π4α=，所以π4α=时，直线1M B ''与直线DC【点睛】方法点睛：证明面面垂直常用的方法：（1）面面垂直的定义；（2）面面垂直的判定定理.在证明面面垂直时，一般假设面面垂直成立，然后利用面面垂直转化为线面垂直，即为所证的线面垂直，组织论据证明即可.19．(1)15224；(2)①分布列见解析，数学期望为165；②答案见解析.【分析】（1）根据给定条件，利用古典概率，结合事件的独立性及组合计数问题列式求解.（2）①求出X 的可能取值及对应的概率，列出分布列并求出期望；②按k n =和k n <分类求出()P X m =的表达式，再建立不等式求出对应的整数m .【详解】（1）设事件A =“该社团只有小明同学同时收到甲、乙两人所发活动通知信息”，所以22753388C C 15()C C 224P A ==.（2）①X 的可能取值为2，3，4，211122554353222222555555C C C C C C 133(2),(3),(4)C C 10C C 5C C 10P X P X P X =========，所以X 的分布列为：X234P 11035310答案第15页，共15页数学期望13316()234105105E X =⨯+⨯+⨯=.②当k n =时，m 只能取n ，此时有()()1P X m P X n ====；当k n <时，整数m 满足k m t ≤≤，其中t 是2k 和n 中的较小者，由甲和乙各自独立、随机地发送活动信息给k 位同学，得所包含的基本事件总数为2(C )k n ，当X m =时，同时收到甲乙两人所发信息的学生人数为2k m -，仅收到李老师或张老师转发信息的学生人数为m k -，由分步乘法原理知，事件{}X m =所包含的基本事件数为2C C C C C C k k m m k k m k m k n k n k n k n k ------=，22C C C C C ()(C )C k k m m k m k m k n k n k k n k k k n nP X m ------===，当k m t ≤<时，22(1)()(1)(1)()(2)22k P X m P X m m k n m k m m k n +=≥=+⇔-+≤--⇔≥-+，22(1)()(1)(1)(1)(21)212k P X m P X m m k n m k m m k n +=≥=-⇔-+≤-+-+⇔≤+-+，因此()P X m =取得最大值时，m 满足22(1)(1)22122k k k m k n n ++-≤≤+-++，假如2(1)22k k k t n +≤-≤+成立，则当2(1)k +能被2n +整除时，()P X m =在2(1)22k m k n +=-+和2(1)212k m k n +=+-+处达到最大；当2(1)k +不能被2n +整除时，()P X m =在2(1)2[]2k m k n +=-+处达到最大值（[]x 表示不超过x 的最大整数），下面证明2(1)22k k k t n +≤-≤+：由1k n ≤<，得222(1)1(1)11202222k kn k k k k k k k n n n n +--+-----=≥=≥++++，22(1)(1)2022k n k k n n n +-+--=-<++，则2(1)22k k n n +-<+，显然2(1)222k k k n +-<+，因此2(1)22k k k t n +≤-≤+.【点睛】关键点点睛：求使()P X m =取得最大值的m 值，关键是求出()P X m =的表达式，再利用最大概率问题求解.。
黑龙江省哈尔滨市第三中学校2022-2023学年高二上学期第三次验收考试英语试题
黑龙江省哈尔滨市第三中学校2022-2023学年高二上学期第三次验收考试英语试题一、短对话1．What are the speakers mainly talking about?A．How to cut a pizza.B．When to have lunch.C．What to eat for lunch.2．What does the man probably do?A．An engineer.B．A teacher.C．A police officer.3．When was the show due to start?A．At 8:00 pm.B．At 9:00 pm.C．At 11:00 pm.4．Where are the speakers?A．At home.B．At a restaurant.C．At a stadium.5．Why will the man go to the beach?A．For cooking.B．For cleaning.C．For swimming.二、长对话听下面一段长对话，回答小题。
6．What does the woman need to buy?A．Perfume.B．Flowers.C．A birthday card.7．What is the probable relationship between the two speakers?A．Colleagues.B．Brother and sister.C．Teacher and student.听下面一段长对话，回答小题。
8．Why do the speakers have to wake up early?A．They have a bus to catch.B．They have a train to catch.C．They have a flight to catch.9．What did Gary think of his trip to Moscow?A．Satisfying.B．Annoying.C．Disappointing.听下面一段长对话，回答小题。
黑龙江省哈尔滨市第三中学校2024-2025学年高三上学期10月月考英语试题
黑龙江省哈尔滨市第三中学校2024-2025学年高三上学期10月月考英语试题一、阅读理解These beautiful reading spots rank among the top 10 of the world’s 50 best libraries and are the inhabitants of your favorite fictional world.Women’s Library, GlasgowRows of books on women’s issues throughout history line the shelves of the only official museum in the UK dedicated to women’s lives, histories and achievements. A number of events across the year transform this library into a living social hub by providing creative writing classes, performance groups and craft sessions. Its key aim is to support women, with services teaching literacy, calculations, and handling a range of issues which include poverty, and surviving violence.Sir Duncan Rice Library, AberdeenThe outside of the modern facility is a huge glass structure made of 760 glass panels and 2.200 tons of steel. Sir Duncan Rice is also conscious of its carbon footprint, designed to collect rainwater which is reused to flush its toilets, harvesting power through solar cells on the roof and using timers to control the use of its fluorescent lighting.Wellcome Reading Room, LondonSpend an afternoon studying in the Reading Room of London’s Wellcome Museum and you may just find yourself immersed in literature. With drawing classes and static artistic displays accompanying rows of educational books, it’s an enjoyable spot to visit and revisit. The impressive stairway and desks are allowing you the perfect spot to pause and reflect, whatever your library mission.John Ryland, ManchesterCreated over 100 years ago, it has grown to become the third largest academic library in the UK, home to over a million manuscripts. Modern extensions to the building added since the 2000s create a breath-taking collision of historic and modern architecture. Regular events planned with the whole family in mind make this library one to visit time and time again.1．What do we know about Women’s Library?A．It is a good place for women to escape violence.B．It serves as the only official museum in Glasgow.C．It promotes women’s education and social contact.D．It boasts various events and a long history.2．Where can you attend classes and view exhibitions?A．In Women’s Library.B．In Sir Duncan Rice Library.C．In Wellcome Reading Room.D．In John Ryland Library.3．What do John Ryland Library and Sir Duncan Rice Library have in common?A．Eco-friendly technologies.B．Events intended for family.C．Extensive collection.D．Special architectural design.The idea of climbing Mt.Qomolangma disgusted me. The mountain came to represent the opposite of everything that I loved and respected about climbing. What had once been the final mountain climbing goal became the focus of a commercial guiding industry. Over the years, the crowds at Base Camp grew, leaving behind tons of trash. Whenever I was asked whether I’d climb Mt. Qomolangma, my answer was always the same: not interested.That was probably where my personal Mt. Qomolangma story would have ended, were it not for an old friend Thom Pollard and his obsession (迷恋) with one of the greatest mysteries. In 1999, he began to explore and found the remains of George Mallory, the celebrated British climber who disappeared while he was attempting to be the first to climb Mt. Qomolangma. But Mallory’s partner, Sandy Irvine, and the camera he had likely carried, were not found. The mountain climbing world has been wondering whether they might have reached the top in 1924.Pollard’s story moved me. I began to pack for the climb and expected that our advanced equipment would make it manageable, perhaps easy. I was wrong. On the highest point on the planet, I was more tired than I’d ever been in any climbing. Along the way, I continuously tipped my hat, not just to Mallory and Irvine but to anyone who has the drive to push himself or herself up this route. My search was in vain, but I began to reconsider Mt. Qomolangma.I witnessed many climbers, who were much more than just self-centered tourists. We shared route information, weather forecasts, and family photos—all united around a common goal.I went to Mt. Qomolangma to seek Irvine. But in the end, I found something more difficult to get: the spirit that Irvine and Mallory shared. It was hiding in plain sight, right where it has always been: inside the brave souls who risk so much to follow in storied adventurers’ footsteps up Mt. Qomolangma.4．Why did the author once hate climbing Mt. Qomolangma?A．Because the mountain was overcrowded.B．Because his original climbing goal changed.C．Because climbing it became a profit-driven industry.D．Because he had to brave the elements on the mountain.5．What motivated the author to climb Mt. Qomolangma later?A．The influence of Thom Pollard.B．The results of the previous climbing.C．The development of advanced equipment.D．The spirit of George Mallory and Sandy Irvine.6．What does the underlined phrase “tipped my hat” in paragraph 3 mean?A．Relieved my tiredness.B．Showed my respect.C．Expressed my gratitude.D．Proved my determination.7．What message does the passage mainly convey?A．The search for missing adventurers holds great value.B．Modern climbing lacks respect for the natural environment.C．Spirits of the climbers of Mt. Qomolangma are worth respect.D．Experienced climbers are qualified to conquer Mt. Qomolangma.A strange sound called “biotwang” was first heard bouncing around the Mariana Trench 10 years ago, and scientists have finally figured out where it comes from.Recorded by microphones deep in the ocean, the unexplained sound — a low, loud moan (哼声) followed by a mechanical echo, like a frog burping (打嗝) in space — thundered through a computer speaker about a decade ago. Confused researchers called it the “biotwang”.“You’ve got this low-frequency portion, like a moan,” says Lauren Harrell, a data scientist at Google Research’s AI for Social Good, adding her own impression of a hearty sigh. “Then youhave the higher-frequency component that sounds, to me, like an outer planet spacecraft — the ‘bip boo, bip boo’ sound.”Confirming which marine animal makes a strange noise isn’t easy, though: it requires a person on a boat to see and identify the source at exactly the same time the sound is heard. “It takes a lot of time, a lot of effort and a fair amount of luck,” Allen says.An international team headed by Allen, marine biologist from Swiss Federal Institute of Technology in Zurich, and Harrell conducted a collaborative research in 2020. While surveying whales off the Mariana Islands, Allen and other researchers saw a mysterious species called the Bryde’s whale 10 times. These whales are spread out far across the huge open ocean, so it’s hard for scientists to observe or study them. On nine of the occasions that Bryde’s whales turned up, the researchers also heard the biotwang. “Once, it’s a coincidence,” Allen says. “Twice is happenstance. Nine times, it’s definitely a Bryde’s whale.”After identifying the source, they reviewed years of audio data from underwater hydrophones to find out where this specific whale sound had previously been heard. “Once scientists know where and when these whales travel,” Harrell says, “AI models could connect that data to climate and environmental factors and thus support protection efforts.”The technology isn’t perfect, though. “These algorithms (算法) can only search for a frequency they know,” says Harrell. “The Bryde’s whale vocalizations change over time and between populations. But because the tools are open-source, other scientists can use them to discover more about whale language. We seem to be so disconnected from, or simply have no access to this amazing underwater world of sound,” he says. “I think it’s about time that we change that.”8．Why is it difficult to identify the source of biotwang?A．Because years of audio data need to be analyzed.B．Because enough time and a right moment are a must.C．Because researchers lack a knowledge of marine animals.D．Because biotwang alternates with low and high frequency9．What is paragraph 5 mainly about?A．Who solved the biotwang mystery.B．When the Bryde’s whale usually appeared.C．How the source of biotwang was determined.D．Why the Bryde’s whale was difficult to observe.10．What is Harrell’s attitude toward their team’s discovery?A．Ambiguous.B．Objective.C．Unconcerned.D．Disapproving. 11．What can be the suitable title for the passage?A．Mystery of Biotwang Finally SolvedB．AI Algorithms Applied in Biotwang ResearchC．Singer of the Deep Ocean — Bryde’s WhaleD．Protection of the Deep Ocean — A Long Way to Go“It won’t forgive your mistakes,” wrote Valentin Lebedev, an astronaut, in his diary. “Even eating becomes more complicated. You must be careful and rely on sealed containers and specialized utensils to open packages. Spills can be dangerous as food particles or liquids might float into equipment or get into your eyes or nose.” Enough to say the anxiety of an altogether different order in zero gravity.What’s worse, in space, no one can hear you scream about travel delays. When will I get back? Such is the dilemma of Butch Wilmore and Suni Williams, two astronauts who have been stranded (被滞留的) on the International Space Station (ISS) since docking there on June 6, 2024. NASA does not like that word. As one official insisted, “I want to make it very clear that Butch and Suni are not stranded in space.”Mr Wilmore and Ms Williams arrived at the ISS aboard the first crewed flight of Boeing’s Starliner. What was meant to be an eight-day stay is approaching the three-month mark after their capsule leaked helium (氦) and five of its 28 engines malfunctioned. That has delayed their return, possibly until February 1, 2025. Precisely what happens now depends on whether NASA thinks Starliner is safe — tests are ongoing — or whether they are better off getting a ride home on a flight operated by Boeing’s competitor, SpaceX. A decision should come soon.The next SpaceX Dragon capsule is due to dock at the ISS in September and return to Earth next year. If it is to make room for Mr Wilmore and Ms Williams, it will go up with two crew members instead of its usual four. That would require Starliner to leave the ISS uncrewed. Boeing says this is not currently possible owing to software issues.As it is, the engineering fault is a shame for Boeing and NASA．If crewed Starliner flights are unworkable, that will put paid to NASA’s ambition for competition in the task of ferrying astronauts to the space station and back to Earth. Now SpaceX looks like the only American game in town capable of getting to and from the ISS.Having a mission prolonged unexpectedly, which sometimes happens, means missing out on changes big and small. Sergei Krikalev spent five extra months on the Mir space station when earthlings got distracted by the breaking up of the Soviet Union. He came back to a whole new world in 1992.12．Which of the following best describes Valentin’s feeling in the diary?A．Amused but fragile.B．Uncomfortable and tense.C．Disturbed but magical.D．Restless and tolerant.13．When did Starliner plan to return at first?A．June 6, 2024.B．June 14, 2024.C．September 6, 2024.D．February 1, 2025.14．What do we know about NASA according to the text?A．It should have made massive investment for Starliner.B．It prefers cooperation with Space X instead of Boeing.C．It is giving a test to fix gas leak and an engineering fault.D．It denied the delayed flight in protection of its reputation.15．What does the last paragraph imply?A．A stranded flight caused Soviet Union to break up.B．What’s in store for Butch and Suni remains to be seen.C．Astronauts will see a whole new world when they return.D．Soviet Union’s spacecraft technology was no better than NASA’s.Always the Outsider?One of the things I used to fear was being the new girl in the office — in the kitchen making coffee while the in-crowd chatted about the weekend. I worried that I wasn’t good enough or smart enough. 16 I’d struggle for words while trying to look cool. Back at school, I was best friends with Kate and Cathy until we had to walk across the road in twos, and guess whowas left out? I’ve always been the outsider from school days to office life. Or is that the story I have told myself?As in so many areas of life, the only thing you can control is your response. I remind myself of what Eleanor Roosevelt said: No one can make you feel lower without your agreement. 17 These are the lessons I have learned along the way ：·Starting anywhere new, you just have to find your people, the ones that get you. 18 It’s OK to take your time and figure out if you’re the right fit for each other. Have faith that you will find the right people for you.·Very often it’s our belief systems that tell us we don’t fit in. We are replaying the stories from childhood and need to rewrite the script (剧本). 19 For example, when are you assuming that you’ll be on your own? What fears are you projecting onto yourself?·Practice self-acceptance. Remind yourself that it’s OK to have a different way of operating in the world.· 20 Never forget that while you might be trying to fit in, you should never try to be anybody but yourself.A．Don’t over-think people or situation.B．Don’t charge into friendships, though.C．Start noticing your patterns of mentality.D．If I was asked a question, panic would set in.E．The only person making you feel like an outsider is you.F．The feeling of being an outsider would force me to shut up.G．We all feel a little lost and awkward sometimes — you’re not alone.二、完形填空I’ve been barefoot in London every day since March last year. Living in a city, I 21 the element of the unexpected. It was as though I’d discovered an extra sense. Travelling on the tube barefoot was 22 at first because there are so many different surfaces. It’s as if I’ve reached a new dimension most people 23 never experience.I took early retirement with a good pension in 2009. These days, I do a lot of 24work. I volunteered to 25 pharmacy (药房) prescriptions to those living in a block of 50 flats in Peckham Rye, who needed medical supplies badly during the pandemic. The block had just undergone restoration and was looking brand new. All the walkways had been 26 , which felt absolutely amazing on my bare feet.Many people offered me 27 during the cold spell, because they thought it was weird behavior. However, I always stayed 28 and told them it was a lifestyle choice. It certainly started interesting 29 with me and at least people were curious.Being outside, being barefoot, 30 people — I’m sure it’s all connected. I’ve been diagnosed with depression. Thanks to this experience, I 31 that being involved with the community and being in nature really assisted with my 32 .Being barefoot makes me feel more 33 and helps with my well-being. Almost no one else seems to have an idea how 34 it feels and it’s the most interesting when done in a city. I’ll never 35 wearing shoes again.21．A．hate B．question C．fear D．love 22．A．novel B．successful C．embarrassing D．essential 23．A．originally B．gradually C．normally D．secretly 24．A．rescue B．community C．investigation D．gardening 25．A．award B．read C．teach D．deliver 26．A．resurfaced B．removed C．blocked D．marked 27．A．shelter B．food C．shoes D．clothes 28．A．alarmed B．calm C．anxious D．concerned 29．A．arguments B．conversations C．hobbies D．games 30．A．greeting B．watching C．helping D．attracting 31．A．discovered B．suspected C．imagined D．predicted 32．A．identity B．growth C．recovery D．study 33．A．exhausted B．learned C．stuck D．grounded 34．A．hard B．uneasy C．incredible D．efficient 35．A．look back to B．go back to C．get down to D．give in to三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。
黑龙江省哈尔滨第三中学校2023-2024学年高二上学期第二次验收考试英语试题(含答案,含听力原文)
黑龙江省哈尔滨第三中学校2023-2024学年高二上学期第二次验收考试英语试题（含答案，含听力原文）哈三中2023-2024学年度上学期高二学年第二次验收考试英语试卷(考试时间：120分钟试卷满分：150分)注意事项：本试卷分第一部分(听力)，第二部分(阅读理解)，第三部分(完形填空)，第四部分(单句填空)，第五部分(篇章语法填空)，第六部分(写作)。
第一部分：听力(共两节，每小题1.5分，满分30分)第一节(共5小题；每小题1.5分.满分7.5分)听下面5段对话。
每段对话后有一个小题，从题中给出的A，B.C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题，每段对话仅读一遍。
1. What does the man want to buyA. A soft drink.B. A movie ticket.C. Some popcorn.2. What does the woman meanA. She wants to try the restaurant.B. She will treat the man.C. She likes to eat out.3. What are the speakers mainly talking aboutA. When the T-shirts will arrive.B. How the quality of T-shirts is.C. Whether they should order more T-shirts.4. What is the woman most likely to do todayA. Visit a lake.B. Stay at homeC. Go to Mumbai.5. Why does the man come to the companyA. To attend an interview.B. To make an appointment.C. To visit the woman.第二节(共15小题：每小题1.5分，满分22.5分)听下面5段对话或独白。
黑龙江省哈尔滨市第三中学2022-2023学年高二上学期开学验收考试数学试题
黑龙江省哈尔滨市第三中学2022-2023学年高二上学期开学验收考试数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题A ．210B ．410C ．5．已知i 为虚数单位，若复数()1i i,z z =-为z 的共轭复数，则A ．13i22+B ．13i22-C ．6．某校为了解学生的课外锻炼身体的情况，随机抽取了部分学生，对他们一周的课外锻炼时间进行了统计，统计数据如表所示，则该校学生一周进行课外锻炼的时间的第A ．2000元B ．2500元C ．3000元8．如图①，在Rt △ABC 中，2C π=，2AC BC ==，D ，△ADE 沿DE 折起到OA ，DE 的位置，使1A D CD ⊥，如图②．若M 在线段1A D 上运动，则当直线CM 与平面DEF 所成角最小时，四面体是（）A．112BC．212D二、多选题9．对于一个古典概型的样本空间Ω和事件,A B()()()()()(),,,,,Cn n A n B n C n A B n AW U U分别表示样本空间A B⋃，事件A CU包含的样本点个数，已知(nΩ()()16n A B n A C⋃=⋃=，则（）A．事件A与B互斥BC．事件A与C互斥D10．某货轮在A处看灯塔B在货轮北偏东75︒，距离为货轮的北偏西30︒，距离为83nmile.货轮由A处向正北航行到偏东60︒，则下列说法正确的是（）A．A处与D处之间的距离是24nmile BC．灯塔C在D处的西偏南60︒D11．如图，在四棱锥P ABCD－中，底面ABCD三角形，且平面PAD⊥平面ABCD，则下列说法正确的是（A．在棱AD上存在点B．异面直线AD与C．二面角P BC-－D．BD⊥平面PAC四、双空题五、解答题（1）证明：//EF 平面11AC D ；（2）求三棱锥11C A C D -的体积．19．哈尔滨地铁第一条线路于2013有“高寒地铁”系统的城市，截止目前，哈尔滨地铁开通运营线路共有三条，分别为线，2号线，3号线，为全市人民出行带来了便捷，某社团小组在一高峰时段对某座地铁站随机抽取了100名乘客，统计其乘车等待时间（等待时间不超过下频率分布直方图.(1)求样本中等待时间大于15分钟的人数及x 的值；(2)根据频率分布直方图，估计这100名乘客等待时间的：（i ）中位数（结果用分数表示）；（ii ）平均值（各组区间的数据以该组区间的中间值作代表）20．记ABC 的内角,,A B C 的对边分别为,,a b c (1)证明：2222a b c =+；(2)若255,cos 31a A ==，求ABC 的周长．21．已知正四棱柱1111ABCD A B C D -中，AB =(1)求证：1BD AC ⊥；(2)求二面角11A A C D --的余弦值；(3)在线段1CC 上是否存在点若不存在，请说明理由.22．2016年起，春节期间全国流行在微信群里发红包为人们工作和生活里很重要的决策方式，包50个，产生的手气红包频数分布表如下：金额分组(]0,5(5,10频数39(1)求产生的手气红包的金额超过。
超实用高考英语复习：专题02 代词、冠词和数词-100题组合练 (原卷版)
专题02 代词、冠词和数词冲关练100题（解析版）距离高考还有一段时间，不少有经验的老师都会提醒考生，愈是临近高考，能否咬紧牙关、学会自我调节，态度是否主动积极，安排是否科学合理，能不能保持良好的心态、以饱满的情绪迎接挑战，其效果往往大不一样。
以下是本人从事10多年教学经验总结出的以下学习资料，希望可以帮助大家提高答题的正确率，希望对你有所帮助，有志者事竟成！养成良好的答题习惯，是决定高考英语成败的决定性因素之一。
做题前，要认真阅读题目要求、题干和选项，并对答案内容作出合理预测;答题时，切忌跟着感觉走，最好按照题目序号来做，不会的或存在疑问的，要做好标记，要善于发现，找到题目的题眼所在，规范答题，书写工整;答题完毕时，要认真检查，查漏补缺，纠正错误。
总之，在最后的复习阶段，学生们不要加大练习量。
在这个时候，学生要尽快找到适合自己的答题方式，最重要的是以平常心去面对考试。
英语最后的复习要树立信心，考试的时候遇到难题要想“别人也难”，遇到容易的则要想“细心审题”。
越到最后，考生越要回归基础，单词最好再梳理一遍，这样有利于提高阅读理解的效率。
另附高考复习方法和考前30天冲刺复习方法。
目录●用单词的适当形式完成句子●单项选择●用单词的适当形式完成短文一用单词的适当形式完成句子1．（广东省东莞市2022-2023学年高二上学期七校联考英语试题）Students should be encouraged to develop good habits and better behave_________ (they).2．（湖南省长沙市雅礼教育集团2022-2023学年高二上学期期中考试英语试题）I couldn’t believe ________ when I heard he did around 250 paintings of the same water lily pond, all indifferent colours and styles.3．（广东省东莞市第四高级中学2022-2023学年高二上学期期中英语试题）They took a pleasant journey to Sanya last week, where the blue water literally took___________(they) breath away with its exceptional beauty.4．（四川省遂宁市射洪中学2022-2023学年高二上学期第一次月考（10月）英语试题）You can rely on ________that he’ll come to meet you on time.5．（北师大版2022选择性必修三Unit8Lesson320,000LeaguesUndertheSea）__________ seems most houses have been destroyed by the storm.6．（北师大版2022选择性必修三Unit9Lesson3EpidemicsExplained）It is estimated ________up to 60% of the local population is being reached through these radio broadcasts.7．（北师大版2022选择性必修三Unit8Lesson2Poetry）He stretched ________ (he) out on the sofa and fell asleep.8．（北师大版2022选择性必修三Unit7Lesson1EQ：IQ）You could not take back a book to the library on the same day you’d taken it out; ________ made no difference to her that you’d read every word in it and needed another to start.9．（北师大版2022选择性必修三Unit7Lesson1EQ：IQ）________ is suggested that on no occasion should you tell other people the password of your email account.10．（北师大版2022选择性必修三Unit8WritingWorkshop~ReadingClub2）I just took _________ for granted that he’d always be around.11．（四川省成都外国语学校2022-2023学年高二上学期期中考试英语试题（含听力））Though our economy grows fast, we produce more than 30 times as much rubbish ________ we did 20 years ago.12．（牛津译林版2022选择性必修三Unit2Integratedskills，Extendedreading，Project，Assessment&Furtherstudy）But when I tried to step forward, I found I was carried________(two) as far as on the Earth and fell over.13．（牛津译林版2022选择性必修三Unit2Integratedskills，Extendedreading，Project，Assessment&Furtherstudy）The number of students now in this school is four times________ it was ten years ago.14．（四川省成都外国语学校2022-2023学年高二上学期期中考试英语试题）I clearly remember my mother saying that sometimes it’s kinder to tell a white lie than to tell ________ truth.15．（广东省佛山市南海区2022-2023学年高二上学期学业水平测试英语试题）Iwas________only girl in a rugby club of 250 boys.16．（广东省茂名市电白区2022--2022学年高二上学期期中考试英语试题）The woman beat the boy on ________ back.17．（北京市中国人民大学附属中学2022-2023学年高二上学期期中考试英语试题）Zhongyuan Festival, or Ghost Festival, is not a sad day, but time to celebrate ____________reunion (重聚) of families.18．（北京市第十三中学2022~2023学年高二上学期期中测试英语试题）I was ______ only girl in a rugby club of 200 boys.19．（黑龙江省哈尔滨师范大学附属中学2022-2023学年高二上学期10月月考英语试题）He put me on ______ spot a bit because h e invited me right in front of his mum and I didn’t particularly want to go.20．（湖南省雅礼中学2022-2023学年高二上学期第一次质量检测英语试题）1 watched a performance of Butterfly Lovers,______beautiful violin concerto composed by He Zhanhao and Chen Gang.21．（黑龙江省双鸭山市第一中学2022-2023学年高二10月月考英语试题）This flat is ________ far cry from the house they had before.22．（牛津译林版2022选择性必修三Unit3Welcometotheunit&Reading）The truck was carrying______________（load）of apples.23．（北师大版2022选择性必修三Unit7Lesson1EQ：IQ）It is clearly stated ________ these regulations apply to everyone in the neighbourhood, without exception.24．（江苏省淮安市淮海中学2022-2023学年高二上学期收心考试英语试卷）To our great relief, the army immediately came to ________ (they) rescue.25．（广东省陆丰市林啟恩纪念中学2022-2023学年高二下学期第二次段考英语试题）With so many different forms of poetry to choose from, you may want to write poems of your own. Give________ a try.26．（黑龙江省哈尔滨第三中学2022-2023学年高二上学期开学测验英语试题）When the Snow White came to herself, she found ________ (she) surrounded by seven dwarves.27．（黑龙江省双鸭山市第一中学2022-2023学年高二上学期开学考试英语试题）_____________never occurred to me that he would fail in the exam.28．（江苏省淮安市淮海中学2022-2023学年高二上学期收心考试英语试卷）Her father was a doctor and threw ________ (he) into fighting the epidemic.29．（北师大版2022选择性必修二Unit4WritingWorkshop-ReadingClub）________suddenly hit him that he could join the charity to help the homeless.30．（北师大版2022选择性必修二Unit5Lesson3Understanding）She admitted that she abandoned ________(she) to a life of pleasure.31．（牛津译林版2022选择性必修二Unit1Integratedskills,Extendedreading,Project,Assessment&Furtherstudy）—Where is Jimmy? —Just now I saw him sitting under the tree, and absorbing ________ (he) in his games.32．（牛津译林版2022选择性必修二Unit3Welcometotheunit&Reading）If you apply ________(you) to the job in hand, you’ll soon finish it.33．（北师大版2022选择性必修二Unit4Lesson3MyFavouriteComedian）They arebusying____________(they)in tidying up the table.34．（北师大版2022选择性必修二Unit5Lesson2TheObjectivesOfEducation）It is unwise to expose________(you)by trying to perform music that is too difficult for you.35．（译林版2022选择性必修四Unit4Extendedreading&Project）Emma frowned, making an effort to compose ________(her).36．（译林版2022选择性必修四Unit4Integratedskills，Extendedreading，Project，Assessment&Furtherstudy）After resting his elbow on the table, he composed_________(he) to listen to my account of the story.37．（译林版2022选择性必修四Unit4Integratedskills，Extendedreading，Project，Assessment&Furtherstudy）Compose __________ (you) and try to tell me what happened.38．（北师大版2022选择性必修三Unit7MeettheNewBoss:YOU）Almost ___________ of us could solve the math problem, for it is too difficult.39．（四川省成都外国语学校2022-2023学年高二下学期期中考试英语试题）Su Bingtian’s breaking the Asian record in the Olympic Games was an exciting moment, _________that impressed us a lot.40．（山西省晋城市第一中学2022-2023学年高二下学期第一次（高二第九次）调研考试英语试题）“Excuse me, I want to have my watch fixed, but I can’t find a repair shop.” “I know ______ nearby. Come on, I’ll show you.”41．（北师大版2022选择性必修三Unit9Lesson3EpidemicsExplained）As_________ result, she says, some of the injuries associated with running, such as runner’s knee, are uncommon among race walkers.42．（北师大版2022选择性必修三Unit9Lesson3EpidemicsExplained）I know him well enough to form________ estimate of his abilities.43．（北师大版2022选择性必修三Unit8Lesson2Poetry）The dentist can usually spot the reason at ________ glance. We’d better get to him fast.44．（北师大版2022选择性必修三Unit8TopicTalk）He lived in _________ time when the blind couldn’t get much education.45．（北师大版2022选择性必修三Unit8TopicTalk）You might also design ________ adventure challenge to train young volunteers.46．（北师大版2022选择性必修三Unit7Lesson1EQ：IQ）A group of young pioneers always accompany ________ disabled girl on her way to school.47．（北师大版2022选择性必修三Unit7Lesson1EQ：IQ）We can make ________ prediction that the historical event is likely to occur again.48．（北师大版2022选择性必修三Unit7WritingWorkshop&ReadingClub2）At the next table he could see ________ elderly lady talking with a policeman.49．（北师大版2022选择性必修三Unit9WritingWorkshop～ReadingClub2）Police have arrested________ suspect in a series of killings in the city.50．（北师大版2022选择性必修三Unit7Lesson3MeettheNewBoss：YOU）History is much more than the study of dusty old objects and events long past. It is _________ essential part of who we are today and who we will become. (用适当的词填空)51．（牛津译林版2022选择性必修三Unit3Welcometotheunit&Reading）Our newspaperis______________ influential newspaper in this city.52．（牛津译林版2022选择性必修三Unit2Grammarandusage）The crisis is entering________crucial, critical phase.53．（牛津译林版2022选择性必修二Unit4Welcometotheunit&Reading）More wind power stations will spring up to meet ________ demand for clean energy.54．（牛津译林版2022选择性必修二Unit1Integratedskills,Extendedreading,Project,Assessment&Furtherstudy）I bought a second-hand computer for only 20 dollars in a sale; it was really _________ good purchase.55．（牛津译林版2022选择性必修二Unit4Grammarandusage）Experts say that the quality of praise is more important than ________ quantity.56．（译林版2022选择性必修四Unit1单元归纳与提升）He came here without friends or possessions but made ________ fortune in the business of diamonds later.57．（广东省东莞市（丰泰外国语、麻涌、七中、清溪、塘厦）2022-2023学年高二上学期期中五校联考期中英语试题）It’s__________great comfort to have a substitute family to be with when you are in a foreign country.58．（广东省东莞市东华松山湖高级中学2022-2023学年高二上学期第一次阶段考试英语试题）Wearing facial masks is ________________ effective way to avoid the infection from the epidemic.59．（牛津译林版2022选择性必修二Unit3Welcometotheunit&Reading）Some researchers point out that daydreaming is ________means of relaxation.二单项选择60．（甘肃省天水市秦州区天水市第一中学2022-2023学年高二上学期12月月考英语试题）To tell ________ truth, Tracy’s room is really ________ mess.A．/; a B．the; / C．the; a D．/; /61．（上海市复旦大学附属中学2022-2023学年高二上学期期中英语试卷）The most important thing about cotton in history is _______ part that it played in _______ Industrial Revolution.A．/ ... / B．the ... / C．a ... the D．the ... the62．（广东省深圳市六校联盟2022-2023学年高二上学期期中考试英语试题）At present there are ________ total of 300 paintings created by the local artists on ________ display in the city gallery. A．the; 不填B．the; a C．a; 不填D．a; a63．（广州市第二中学2022-2023学年高二上学期12月月考英语试题）They acknowledge________, in a few cases, home schooling offers educational opportunities superior to ________ found in most public schools, but few parents can provide such educational advantages. A．where; ones B．that; those C．that; them D．what; which64．（上海市复旦大学附属中学2022-2023学年高二上学期期中英语试卷）The owner and captain discussed it with _______ colleagues.A．its B．their C．her D．him65．（上海市复旦大学附属中学2022-2023学年高二上学期期中英语试卷）At a rough estimate, Nigeria is _______ Great Britain.A．three times the size of B．three times the size asC．three times as the size of D．three times what the size of。
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哈三中2022-2023学年度上学期高二学年第二次验收考试英语试卷第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中给出的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间回答有关小题和阅读下一小题。
每段对话仅读一遍。
例：How much is the shirt？A.f 19.15.B.£9.15.C.£9.18.答案是B.1.What do we learn from the conversation?A.The man hates to lend his tools to other people.B.The man hasn't finished working on the bookshelf.C.The man lost those tools.2.What are the two speakers talking about?A.A park.B.A trip.C.A cinema.3.What does the man mean?A.He would like to make an appointment for the woman.B. He thinks it worthwhile to try Santerbale's.C.He knows a less expensive place for a haircut.4. What do we learn from this conversation?A.The man wants to go to Los Angeles.B.The man wants to go to San Francisco.C.There are no flights to Los Angeles for the rest of the day.5.What is the woman's opinion of the research paper?A. It's fine as it is.B. Only a few changes should be made in it.C. Major revisions are needed in it.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6至8题。
6.Why is Ken calling?A.To ask about the address for the meeting.B. To ask about the time for the meeting.C.To remind Andy of the meeting.7.Where is Andy?A. In his office.B. In the supermarket.C.In the downtown.8. What is Ken's phone number?A.439-808-7754.B.493-908-7754.C.439-908-7754.听第7段材料，回答第9至11题。
9. Which of the following is the man's favorite food?A.Carrots.B.Chocolate cakes.C.Fruits.10. What are the two speakers probably doing now?A. Having a meal.B.Shopping.C.Preparing food.11. What does the woman say about carrots?A. It is rich in fibers.B. It can reduce weight.C. It contains much vitamin C.听第8段材料，回答第12至14题。
12.Where is the conversation taking place?A. In the man's house.B.In the woman's house.C. In their friend's house.13. What color is the meat container?A.Blue.B.Yellow.C.Red.14. What is the side dish mentioned by the man?A. Eggplant with soy sauce.B. Pork with pineapple.C.Tomatoes with sugar.听第9段材料，回答第15至17题。
15.Who is learning Chinese probably?A.Rose.B.Jane.C.Jack.16. How many children does the woman have?A.Three.B.Four.C.Five.17. What will the woman do tomorrow?A.Go to the cinema.B.Go to the McDonald's.C.Go to school.听第10段材料，回答第18至20题。
18.What happened to the speaker?A.He transferred to another post in another city.B. His colleagues started to get along well with him.C.His hard work paid off.19. What contributions did the speaker make for the company?A.He helped increase the sales.B.He helped build a branch company.C.He helped make new products.20.Which of the following statements is TRUE?A. The speaker's pay rose to $15,000 per year.B. The speaker's department sales increased a lot last year.C.The speaker refused the rise.第二部分阅读理解（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。
AIn today's fast-paced world, it's no surprise that everyone is on the hunt for better ways to accomplish more with less online. Thanks to a select few remote collaboration apps, it's now easier than ever to realize the goal regardless of where they are located on the globe.G SuiteG Suite is a term used to describe Google's collection of productivity apps. They include Google Does (similar to Microsoft Word),Google Sheets (similar to Microsoft Excel),and Google Hangouts, which is a web-based meeting platform.Process StreetUsing Process Street helps keep everyone responsible. Those who use Process Street like the way it securely keeps all members award of exactly what they need to do and by when. Team members can track activity from the dashboard and get noted when tasks are done.LoomLoom is a web-based ad-hoc video platform that allows users to record their screens for quick replaying by others. This is great for how-to videos, webinars, and instructional guides. The best part about Loom is that it’s free to use.SkypeSkype is the tried and trusted chatting/ video conferencing platform that has stood the test of time over and over again. Skype. a Microsoft product. allows for fast communication with anyone else who has a login, and it even supports international calling with video. The only downside with Skype is that you need a Microsoft login in order to use it.21. Which app can keep a team well informed of assigned tasks?A.G Suite.B.Process Street.C.Loom.D.Skype.22.What should one do before using Skype?A.Apply for a Microsoft login.C.Update the Microsoft system.23.What do the four apps have in common?A.They are free of charge.C.They are difficult to access.B.Specialize in Microsoft Office.D.Record the Microsoft screens.B.They need to be replayed.D.They can improve efficiency. BThe life of a premature baby born during the winter storm in Texas was saved thanks to a team of medical professionals, including a doctor and two nurses who traveled from east Austin to Marble Falls in an effort to save a newborn baby's life.When Arias began experiencing pains, she and her parents headed to the closest hospital, Baylor Scott & White. Arias gave birth to her daughter, Zaylynn, who weighed just over onepound and was in need of advanced special care. However, the hospital does not offer thespecialized care premature babies require.“We had five or six people out at the nurses' station calling hospital networks all over the state of Texas,” said Meredith Schubert, the labor and delivery nurse on duty when Arias arrived. “Nobody could answer our cry for help.”They finally reached Dr. John Loyd through a patient, division neonatologist chief at Dell Children's Medical Center in Austin, Texas. Around 5 p.m., after already having worked a full shift, Loyd packed his SUV with equipment and he and two NICU nurses set out for Marble Falls, about 55 miles away. The drive took Loyd and the nurses about two hours as they drove in the night through ice and snow.After safely arriving at the Marble Falls medical center around 8 p.m., the Dell Children's crew set up a temporary newborn ICU. Together, the Dell Children's and Baylor Scott&White teams worked around the clock to care for the mother and daughter.Once the weather cleared enough to allow for a helicopter to safely land, Zaylynn was transferred to Dell Children's, where there is a Level IV newborn intensive care unit.“It was incredible when the helicopter lifted off. There were tears from all of us,”said Schubert. “It was a huge relief and sense of accomplishment and joy that Zaylynn was doing so well and getti ng to the place that she needed to be.”Arias told KVUE that she was grateful to the doctors and nurses who worked together to save her daughter.24.What did the newborn baby need badly?A. Professional surgery.C. Immediate transfer.B.Special intensive nursing.D.Experienced doctors.25.Which word best describes Schubert's cry for help before reaching Loyd?A.Timely.B.Hopeful.C.Desperate.D.Encouraging.26.What was the most touching part about Loyd?A.He came with all the necessary equipment.B.He tried his best to maintain his honor.C.He had enough bravery to drive at night.D. He drove to rescue at night in severe weather.27.What made the doctors and nurses feel a sense of relief?A.The fine weather.C.The takeoff of the helicopter.B. The baby's improvement.D.The baby's arrival at its destination. CAntarctica has actually become a kind of space station-a unique observation post for detecting important changes in the world's environment. Remote from major sources of pollution and the complex geological and ecological systems that are common elsewhere, Antarctica makes possible scientific measurements that are often sharper and easier to interpretthan those made in other parts of the world.Therefore, growing numbers of scientists see Antarctica as a distant-early-warning sensor, where potentially dangerous global trends may be spotted before they show up to the north. One promising field of investigation is glaciology. Scholars from the United States, Switzerland, and France are pursuing seven separate but related projects that reflect their concern for the health of the West Antarctic Ice Sheet-a concern they believe the whole world should share.The Transantarctic Mountain, some of them more than 14,000 feet high, divide the continent into two very different regions. The part of the continent to the “east” of the mountains is a high plateau （高原）covered by an ice sheet nearly two miles thick.“West＂of the mountain, the half of the continent south of the Americas is also covered by an ice sheet, but there the ice rests on rock that is mostly well below sea level. If the West Antarctic Ice Sheet disappeared, the western part of the continent would be reduced to a few and far gathering of island.While ice and snow are obviously central to many environmental experiments, others focus on the mysterious "dry valley" of Antarctica. The valleys contain little ice or snow even in the depths of winter. Through the mountains of southern Victoria Land, these valleys once held enormous glaciers that extended 9.000 feet downside to the Ross Sea. Now the glaciers are gone, perhaps due to the global warming trend during the 10,000 years since the ice age. Even the snow that falls in the dry valleys is blown away by strong winds that roars down from the polar plateau to the sea.Despite the mysterious aspect of the dry valleys. some scientists believe they may carry the hope of the environment. Some scientists believe that in some cases the dry valleys may absorb pollutants faster than pollutants enter them.28. What is the best title for this passage?A. Antarctica and environmental Problems.B. Antarctica: a high plateau.C.Antarctica:a Unique Observation Post.D.Antarctica: a Mysterious Place.29.What would the result be if the West Antarctic Ice Sheet disappeared?A.The western part of the continent would be disappeared.B.The western part of the continent would be reduced.C.The western part of the continent would become a fragmentary island.D.The western part of the continent would be reduced to a gathering of island.30.Why are the Dry Valleys left bare?A.Strong wind blows the snow away.B.It rarely snows.C. Because of the global warming trend and fierce wind.D.Ice sheets.31.Which of the following is true?A.The “Dry Valleys" have nothing left inside.B.The“Dry Valleys” never held glaciers.C.The“Dry Valleys" may carry a message of hope.D.The “Dry Valleys" are useless to scientists.DMass transportation revised the social and economic fabric of the American city in three fundamental ways. It activated physical expansion, it sorted out people and land uses, and it accelerated the instability of urban life. By opening vast areas of unoccupied land for residential expansion，the omnibuses（公共汽车），horse railways，trains，and electric trolleys pulled settled regions outward two to four times more distant form city centers than they were in the premodern era. In 1850. for example. the borders of Boston lay scarcely two miles from the old business district: by the turn of the century they extended ten miles. Now those who could afford it could live far from the old city center and still go there for work, shopping, and entertainment. The new accessibility of land around almost every major city sparked an explosion of real estate development and fueled what we now know as urban sprawl. Between 1890 and 1920, for example. some 250,000 new residential lots were recorded within the borders of Chicago, most of them located in distant areas.Over the same period. another 550.000 were plotted outside the city limits but within the metropolitan（都市）area. Anxious to take advantage of these areas，real estate developers added 800,000 potential building sites to the Chicago region in just thirty years-lots that could have housed five to six million people.Of course, many were never occupied: there was always a huge surplus of subdivided, but vacant, land around Chicago and other cities. These demonstrates a feature of residential expansion related to the growth of mass transportation: urban sprawl was essentially unplanned. It was carried out by thousands of small investors who paid little attention to coordinated land use or to future land users.Those who purchased and prepared land for residential purposes, particularly land near or outside city borders did so to create demand as much as to respond to it. Chicago is a typical example of this process. Real estate subdivision there proceeded much faster than population growth.32.With which of the following subjects is the passage mainly concerned?A. Types of mass transportation.B. Instability of urban life.C.How supply and demand determine land use.D. The effect of mass transportation on urban expansion.33. Why does the author mention both Boston and Chicago?A.To demonstrate positive and negative effects of growth.B. To use cities with and without mass transportation as examples.C. To show mass transportation changed many cities.D.To contrast their rate of growth.34.According to the passage, what was one disadvantage of residential expansion?A. It was expensive.B. It happened too slowly.C. It was unplanned.D. It created a demand for public transportation.35.The author mentions Chicago in the second paragraph as an example of a cityA.that is large.B. that is used as a model for land development.C.where the development of land exceeded population growth.D. with an excellent mass transportation system.第二节（共5小题；每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。